Deterministic Optimization Approach Research Articles

RETRACTED: Interval optimization based performance of photovoltaic/wind/FC/electrolyzer/electric vehicles in energy price determination for customers by electricity retailer

Abstract This paper proposes optimal management of hydrogen storage systems and plug-in electric vehicles in the scheduling of retailer under pool market price uncertainty which real-time pricing is determined in comparison with time-of-use pricing and fixed pricing. Also, pool market price uncertainty is modeled via proposed interval optimization approach for uncertainty-based profit function of retailer. In the proposed model, uncertainty-based profit function of retailer is reformulated as a deterministic bi-objective framework with average and deviation profits as the conflict objective functions which deviation profit should be minimized while average profit should be maximized. Furthermore, weighted sum approach is used to solve the proposed bi-objective model in order to obtain Pareto solutions. Finally, fuzzy decision-making approach is provided to select the trade-off solution from Pareto solutions. The proposed MIP-based model is implemented in GAMS software which can be solved using CPLEX solver. Deterministic and interval optimization approaches under fixed, time-of-use, and real-time pricing are utilized in the case studies and the results are compared with each other in order to show the effectiveness of the proposed model. The obtained results show that deviation profit of retailer decreases in the proposed interval optimization approach in comparison with deterministic approach. Also, average profit of retailer increases in the real-time pricing in comparison with time-of-use pricing and fixed pricing.

An Efficient Deterministic Approach to Optimal Design of Reliable Networks

Reliability and cost are two most important issues in network design optimization that is extensively applied into various optimization problems such as supply chain network design, telecommunication network design, and transportation engineering. This paper proposes an efficient deterministic optimization approach for solving the problem of designing a reliable network. The problem discussed in this paper considers the minimization of the total cost subject to demand, flow balance, and capacity constraints while simultaneously employing mitigation resources to reduce the risk of network failures. Such a problem is typically formulated as a nonconvex mixed-integer program that cannot be easily solved to obtain a global optimum. The proposed optimization method transforms the original nonconvex program into a mixed-integer linear program by linearization techniques and is thus guaranteed to reach a global optimum. In addition, an extended model of minimizing the total weighted loss subject to resource constraints is discussed and globally solved by the proposed method. Experimental results show that the proposed approach effectively solves the reliable network design problem with the minimal total cost or the minimal total weighted loss under an appropriate allocation of mitigation resources.

Optimal energy pricing for consumers by electricity retailer

In the smart grid, retail price determination by electricity retailer is necessary in the presence of hydrogen storage systems and plug-in electric vehicles under pool market price uncertainty. Therefore, in this paper, real-time pricing is proposed in comparison with time-of-use pricing and fixed pricing. Furthermore, an interval optimization approach is proposed for pool market price uncertainty modeling. In this approach, uncertainty-based profit function of retailer is reformulated as a deterministic bi-objective problem with average and deviation profits as the conflict objective functions which average profit should be maximized while deviation profit should be minimized. Furthermore, epsilon constraint method is used to solve the proposed bi-objective model in order to obtain Pareto solutions. Finally, fuzzy satisfying approach is used to select the trade-off solution from Pareto solutions. The obtained results show that average profit of retailer increases in the real-time pricing in comparison with time-of-use pricing and fixed pricing. Also, deviation profit of retailer decreases in the proposed interval optimization approach in comparison with deterministic approach. The proposed mixed-integer linear programming model is solved using CPLEX solver under GAMS optimization software. To validate the better performance of proposed model, three types of retail price determination under deterministic and interval optimization approaches are utilized and the results are compared with each other.

Implications of future climatic uncertainty on payments for forest ecosystem services: The case of the East Coast of New Zealand

Forestry’s long-term nature and associated uncertainties play against its consideration in land-use decisions. This study’s objective was assessing the implications of uncertainty on the feasibility of afforesting erodible land with natives. The New Zealand example has global relevance enabling: innovative statistical representation of climatic uncertainty, economic uncertainty analysis due to existing payments for services, and the profitability of long-rotation species due to Māori’s socio-cultural aspirations. We complemented a deterministic optimisation approach with Monte-Carlo methods to identify optimal afforestation areas representing uncertainty probabilistically. With stochastic dominance/efficiency tests, relevant to landowners, we identified that the uncertainty and profitability of long-rotation species increase at low discount rates, plausible due to low opportunity costs and inter-generational aspirations (not possible in competitive circumstances). At low discount rates, the high profitability odds of the long-rotation alternative compensate its high uncertainty and make it the preferred one even for highly risk-averse owners. With a probabilistic cost-benefit analysis, relevant to policymakers, we identified that the benefits necessary to cover erosion-reduction investments would need to be higher than expected to hedge against climatic uncertainty. These results were obtained through the uncertainty analysis. The methods/results covered in this study are relevant to land-use studies/models seeking to measure uncertainty impacts simply.

Profile likelihood-based analyses of infectious disease models.

Ordinary differential equation models are frequently applied to describe the temporal evolution of epidemics. However, ordinary differential equation models are also utilized in other scientific fields. We summarize and transfer state-of-the art approaches from other fields like Systems Biology to infectious disease models. For this purpose, we use a simple SIR model with data from an influenza outbreak at an English boarding school in 1978 and a more complex model of a vector-borne disease with data from the Zika virus outbreak in Colombia in 2015-2016. Besides parameter estimation using a deterministic multistart optimization approach, a multitude of analyses based on the profile likelihood are presented comprising identifiability analysis and model reduction. The analyses were performed using the freely available modeling framework Data2Dynamics (data2dynamics.org) which has been awarded as best performing within the DREAM6 parameter estimation challenge and in the DREAM7 network reconstruction challenge.

Reserve Policy Optimization for Scheduling Wind Energy and Reserve

The rapid increase in the integration of renewable resources has given rise to challenges in power system operations. Due to the uncertainty and variability of renewable generation, additional reserves may be needed to maintain reliability. Uncertainty complicates the process of economic dispatch and renders the deterministic optimization approach less effective. Existing optimization solutions for handling uncertainty, such as scenario-based stochastic programming and robust programming, are also computationally expensive, especially when there are multiple wind farms. Such approaches are less practical for large-scale systems during real-time operations. This paper investigates offline stochastic algorithms to train deterministic operational policies. Such policies are then added to real-time operational models. Specifically, an offline policy generation technique is proposed to provide a stochastic reserve margin to hedge against the real-time uncertainty of (multiple) wind farm generation. The proposed policy generation structure uses a forecast-based framework that accounts for wind generation and system loading conditions. The proposed approach is tested on the Reliability Test System 1996. The proposed approach is compared against existing reserve rules to demonstrate the improvement in handling uncertainty and achieving a more secure solution.

Improving quality control through chance constrained programming: A case study using Bailey method

Worldwide it is an accepted practice that guidelines regarding aggregate gradation to be adopted for any asphalt concrete mixture are recommended by transportation agencies. In general, these specifications are based on past experience and knowledge about local conditions. Alternatively, Bailey method of mixture design considers actual aggregate properties (like shape, density, packing characteristics) while deciding aggregate gradation. Such a mechanistic approach guarantees better mixture performance. As a single source of aggregate cannot meet requirements at all sieve sizes, aggregates from different sources have to be combined to achieve target gradation. Currently used deterministic optimization approaches for aggregate blending use mean values. This leads to a situation where resultant gradation is beyond specification limits occasionally. Alternatively, stochastic optimization approaches consider inherent gradation variability while arriving at final blending proportions. The present work describes a novel chance constrained programming approach that minimizes overall cost of mixture while considering quality control issues. The proposed chance constrained programming approach offers flexibility of introducing various gradation limits as well as Bailey ratio constraints simultaneously. The proposed methodology is validated using Monte Carlo’s simulation approach. The simulation results indicated that mixtures blended using chance constrained approach produce less number of failures when compared to deterministic approach. This is due to the fact that inherent material variability is considered during blend optimization. The proposed work offers advantages of producing asphalt concrete mixtures at lower cost while having better quality control.

Deterministic and Robust Optimization Approach for Single Artillery Unit Fire Scheduling Problem

In this study, deterministic and robust optimization models for single artillery unit fire scheduling are developed to minimize the total enemy threat to friendly forces by considering the enemy target threat level, enemy target destruction time, and target firing preparation time simultaneously. Many factors in war environments are uncertain. In particular, it is difficult to evaluate the threat levels of enemy targets definitively. We consider the threat level of an enemy target to be an uncertain parameter and propose a robust optimization model that minimizes the total enemy threat to friendly forces. The robust optimization model represents a semi-infinite problem that has infinitely many constraints. Therefore, we reformulate the robust optimization model into a tractable robust counterpart formulation with a finite number of constraints. In the robust counterpart formulation with cardinality-constrained uncertainty, the conservativeness and robustness of the solution can be adjusted with an uncertainty degree, Γ. Further, numerical experiments are conducted to verify that the robust counterpart formulation with cardinality-constrained uncertainty can be made equivalent to the deterministic optimization model and the robust counterpart formulation with box uncertainty by setting Γ accordingly.

Bayesian Selection for the $\ell _2$ -Potts Model Regularization Parameter: 1-D Piecewise Constant Signal Denoising

Piecewise constant denoising can be solved either by deterministic optimization approaches, based on the Potts model, or by stochastic Bayesian procedures. The former lead to low computational time but require the selection of a regularization parameter, whose value significantly impacts the achieved solution, and whose automated selection remains an involved and challenging problem. Conversely, fully Bayesian formalisms encapsulate the regularization parameter selection into hierarchical models, at the price of high computational costs. This contribution proposes an operational strategy that combines hierarchical Bayesian and Potts model formulations, with the double aim of automatically tuning the regularization parameter and of maintaining computational effciency. The proposed procedure relies on formally connecting a Bayesian framework to a l2-Potts functional. Behaviors and performance for the proposed piecewise constant denoising and regularization parameter tuning techniques are studied qualitatively and assessed quantitatively, and shown to compare favorably against those of a fully Bayesian hierarchical procedure, both in accuracy and in computational load.

A Two-Stage Robust Optimization for Centralized-Optimal Dispatch of Photovoltaic Inverters in Active Distribution Networks

Optimally dispatching photovoltaic (PV) inverters is an efficient way to avoid overvoltage in active distribution networks, which may occur in the case of the PV generation surplus load demand. Typically, the dispatching optimization objective is to identify critical PV inverters that have the most significant impact on the network voltage level. Following, it ensures the optimal set-points of both active power and reactive power for the selected inverters, guaranteeing the entire system operating constraints (e.g., the network voltage magnitude) within reasonable ranges. However, the intermittent nature of solar PV energy may affect the selection of the critical PV inverters and also the final optimal objective value. In order to address this issue, a two-stage robust centralized-optimal dispatch model is proposed in this paper to achieve a robust PV inverter dispatch solution considering the PV output uncertainties. In addition, the conic relaxation-based branch flow formulation and the column-and-constraint generation algorithm are employed to deal with the proposed robust optimization model. Case studies on a 33-bus distribution network and comparisons with the deterministic optimization approach have demonstrated the effectiveness of the proposed method.

Reliability-based design optimization of reinforced concrete structures with elastomeric isolators

Engineering design optimization aims at designing low-cost systems and structures that fulfill certain performance objectives. In civil engineering Reliability-Based Design Optimization (RBDO) is extremely important because it enables to find optimal structure configurations while considering the effects of uncertainties, such as loading, geometry, structural parameters, modeling assumptions etc., on the building structural performance and reliability. The impact of uncertainties on system response and safety levels may escape the deterministic optimization approach. In this work we perform a multiobjective RBDO of reinforced concrete structures with elastomeric base isolators. Seismic isolation makes a superstructure less susceptible to ground motion caused by earthquakes and reduces the damages on the building. We perform both a sizing optimization of the superstructure (with the beam and column sections and reinforcements as input decision variables) and an optimization of the isolator catalog variables (elastomer rubber type, allowed displacement and dimensions). Uncertainty sources are the vertical loadings and the isolator damping coefficient. We aim at minimizing the superstructure cost as well as minimizing the top floor acceleration and displacement to reduce maintenance costs, while considering probabilistic constraints (and objectives if appropriate). The probabilistic responses are given in terms of percentiles computed with the Polynomial Chaos Expansion (PCE) method [1]. PCE statistical responses can be very accurate but its computational cost is prohibitive for a large number of uncertainties or a high polynomial order. We try to mitigate this effect with an Adaptive Sparse PCE (ASPCE) approach [2] which builds a high-order sparse polynomial with limited sample evaluations. ASPCE reduces the overall computational cost while preserving accuracy. We compare the deterministic optimization and the RBDO results for a base-isolated and a fixed-base structure subject to the same type of actions.

Genetic algorithms for the optimisation of the Schwartz–Smith two-factor model: a case study on a copper deposit

Mining companies typically seek ways to hedge risks affecting their production. One useful instrument to mitigate the financial risk is the futures contracts on commodity prices. Information from the transactions in futures markets is publicly available and can be analysed with the Schwartz–Smith two-factor model (SSTF). However, finding the parameters governing this model can be very challenging. This step is done using a deterministic optimisation approach called the Expectation–Maximisation algorithm (EM). The starting values of the model will have a significant effect on the convergence of the EM. To ensure the solution does not get stuck in a local maximum, the EM algorithm is performed multiple times with different starting values. This paper assesses the value of genetic algorithms (GA) to optimise the parameters of the SWTF model. Although they are slower than EM algorithms because they use random number generators to search for the optimal solution, GA optimise a population of solutions instead of working on only one solution at the time. Moreover, a constraint on the range parameter can be applied to ensure the parameter has a sound economic meaning. Once the SWTF parameters have been calibrated on the observation of futures contracts, the model can be used for the simulation of spot and futures prices. To demonstrate the performance of the proposed approach, a case study was conducted on a copper deposit. The simulations based on the SWTF model whose parameters are determined by GA are used. An active management strategy of the stockpile, dependent on discrepancies in commodity futures prices is tested. Results show that the active management strategy produces positive returns over the passive investment approach.

Operational strategy and planning for raw natural gas refining complexes: Process modeling and global optimization

Optimal operational strategy and planning of a raw natural gas refining complex (RNGRC) is very challenging since it involves highly nonlinear processes, complex thermodynamics, blending, and utility systems. In this article, we first propose a superstructure integrating a utility system for the RNGRC, involving multiple gas feedstocks, and different product specifications. Then, we develop a large‐scale nonconvex mixed‐integer nonlinear programming (MINLP) optimization model. The model incorporates rigorous process models for input and output relations based on fundamentals of thermodynamics and unit operations and accurate models for utility systems. To reduce the noncovex items in the proposed MINLP model, equivalent reformulation techniques are introduced. Finally, the reformulated nonconvex MINLP model is solved to global optimality using state of the art deterministic global optimization approaches. The computational results demonstrate that a significant profit increase is achieved using the proposed approach compared to that from the real operation. © 2016 American Institute of Chemical Engineers AIChE J, 63: 652–668, 2017

Sales plan generation problem on TV broadcasting

Major advertisers and/or advertisement agencies purchase hundreds of slots during a given broadcast period. Deterministic optimization approaches have been well developed for the problem of meeting client requests. The challenging task for the academic research currently is to address optimization problem under uncertainty. This paper is concerned with the sales plan generation problem when the audience levels of advertisement slots are random variables with known probability distributions. There are several constraints the TV networks must meet including client budget, product category and demographic information, plan weighting by week, program mix requirements, and the lengths of advertisement slots desired by the client. We formulate the problem as a chance constrained goal program and we demonstrate that it provides a robust solution with a user specified level of reliability.

A hybrid stochastic–deterministic optimization approach for integrated solvent and process design

The best solution to computer-aided solvent and process design problems can be only achieved by the simultaneous optimization of solvent molecules and process operating conditions. In this contribution, a hybrid stochastic-deterministic optimization approach is proposed for integrated solvent and process design. It is a combination of a genetic algorithm (GA) that optimizes the discrete molecular variables and a gradient-based deterministic algorithm that solves the continuous nonlinear optimization problem of the process at fixed molecular variables as proposed by the GA. The method is demonstrated on a coupled absorption-desorption process where solvent molecular structures as well as the operating conditions of the absorption and desorption columns are optimized simultaneously. While deterministic mixed-integer nonlinear programming (MINLP) algorithms rely on well-selected initial estimates, the proposed hybrid approach can reliably and steadily solve the problem under random initializations. The combination of the advantages of stochastic and deterministic algorithms makes the approach a promising alternative to conventional MINLP algorithms for solving integrated solvent and process design problems.

Integrated gasoline blending and order delivery operations: Part I. short‐term scheduling and global optimization for single and multi‐period operations

Gasoline is one of the most valuable products in an oil refinery and can account for as much as 60–70% of total profit. Optimal integrated scheduling of gasoline blending and order delivery operations can significantly increase profit by avoiding ship demurrage, improving customer satisfaction, minimizing quality give‐aways, reducing costly transitions and slop generation, exploiting low‐quality cuts, and reducing inventory costs. In this article, we first introduce a new unit‐specific event‐based continuous‐time formulation for the integrated treatment of recipes, blending, and scheduling of gasoline blending and order delivery operations. Many operational features are included such as nonidentical parallel blenders, constant blending rate, minimum blend length and amount, blender transition times, multipurpose product tanks, changeovers, and piecewise constant profiles for blend component qualities and feed rates. To address the nonconvexities arising from forcing constant blending rates during a run, we propose a hybrid global optimization approach incorporating a schedule adjustment procedure, iteratively via a mixed‐integer programming and nonlinear programming scheme, and a rigorous deterministic global optimization approach. The computational results demonstrate that our proposed formulation does improve the mixed‐integer linear programming relaxation of Li and Karimi, Ind. Eng. Chem. Res., 2011, 50, 9156–9174. All examples are solved to be 1%‐global optimality with modest computational effort. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2043–2070, 2016

Optimizing Water Allocation under Uncertain System Conditions for Water and Agriculture Future Scenarios in Alfeios River Basin (Greece)—Part B: Fuzzy-Boundary Intervals Combined with Multi-Stage Stochastic Programming Model

Optimal water allocation within a river basin still remains a great modeling challenge for engineers due to various hydrosystem complexities, parameter uncertainties and their interactions. Conventional deterministic optimization approaches have given their place to stochastic, fuzzy and interval-parameter programming approaches and their hybrid combinations for overcoming these difficulties. In many countries, including Mediterranean countries, water resources management is characterized by uncertain, imprecise and limited data because of the absence of permanent measuring systems, inefficient river monitoring and fragmentation of authority responsibilities. A fuzzy-boundary-interval linear programming methodology developed by Li et al. (2010) is selected and applied in the Alfeios river basin (Greece) for optimal water allocation under uncertain system conditions. This methodology combines an ordinary multi-stage stochastic programming with uncertainties expressed as fuzzy-boundary intervals. Upper- and lower-bound solution intervals for optimized water allocation targets and probabilistic water allocations and shortages are estimated under a baseline scenario and four water and agricultural policy future scenarios for an optimistic and a pessimistic attitude of the decision makers. In this work, the uncertainty of the random water inflows is incorporated through the simultaneous generation of stochastic equal-probability hydrologic scenarios at various inflow positions instead of using a scenario-tree approach in the original methodology.

Possibility-Based Multidisciplinary Optimisation For Electric-Powered Unmanned Aerial Vehicle Design

AbstractThis paper describes a possibility-based multidisciplinary optimisation for electric-powered unmanned aerial vehicles (UAVs) design. An in-house integrated UAV (iUAV) analysis program that uses an electric-powered motor was developed and validated by a Predator A configuration for aerodynamics, weight, and performance parameters. An electric-powered propulsion system was proposed to replace a piston engine and fuel with an electric motor, power controllers, and battery from an eco-system point of view. Moreover, an in-house Possibility-Based Design Optimisation (iPBDO) solver was researched and developed to effectively handle uncertainty variables and parameters and to further shift constraints into a feasible design space. A sensitivity analysis was performed to reduce the dimensions of design variables and the computational load during the iPBDO process. Maximising the electric-powered UAV endurance while solving the iPBDO yields more conservative, but more reliable, optimal UAV configuration results than the traditional deterministic optimisation approach. A high fidelity analysis was used to demonstrate the effectiveness of the process by verifying the accuracy of the optimal electric-powered UAV configuration at two possibility index values and a baseline.

A Hybrid Evolutionary–Deterministic Optimization Approach for Conceptual Design

Most optimization-based approaches in conceptual process design either focus on global optimization using simplified process models or utilize some kind of metaheuristic to optimize by means of repetitive runs of a detailed simulation model. Because the design of even a single distillation column model results in a nonconvex large-scale and mixed-integer optimization problem, if rigorous thermodynamic models are applied, deterministic optimization is still mostly limited to local optimization. In order to investigate and improve the solution quality of previously developed efficient local optimization approaches, this paper proposes a hybrid evolutionary–deterministic optimization approach. The resulting memetic algorithm not only allows the optimization of the initial process structure but also facilitates discrete decision making that severely complicates a deterministic optimization due to the resulting discontinuities. The proposed approach not only eases the application by reducing the necessary user...

Analysis of High Torque and Power Densities Outer-Rotor PMFSM with DC Excitation Coil for In-Wheel Direct Drive

In recent years, flux switching machines (FSMs) have been an attractive research topic owing to their tremendous advantages of robust rotor structure, high torque, and high power capability suitable for intensive applications. However, most of the investigations are focusing on the inner-rotor structure, which is incongruous for direct drive applications. In this study, high torque and power densities of a new 12S-14P outer-rotor permanent magnet (PM) FSM with a DC excitation coil was investigated based on two-dimensional finite element analysis for in-wheel direct drive electric vehicle (EV). Based on some design restrictions and specifications, design refinements were conducted on the original design machine by using the deterministic optimization approach. With only 1.0 kg PM, the final design machine achieved the maximum torque and power densities of 12.4 Nm/kg and 5.93 kW/kg, respectively, slightly better than the inner-rotor HEFSM and interior PM synchronous machine design for EV.